It seems confusing what actually happens when you touch the Tesseract. Whenever it has been seen in a Marvel movie, it's either being handled with prongs, contained in some form of a box or carried in a transport capsule probably developed by the Asgardian's.

However, in the ending scenes of Captain America - The First Avenger,

Red Skull touches it with his bare hands and he gets teleported after touching it.

4 Answers
4

This question has an inherent flaw: It confuses two particular pieces of Marvel lore from two different media and makes the assumption they are the same device. The Cosmic Cube and the Tesseract device are two completely different devices.

The Cosmic Cube is a device/immature being of alien origin whose powers of reality alteration allow the use of the cube to make fundamental changes using reality-manipulating abilities inherent in the adult form of the cube.

The Tesseract is an alien device believed to have been created by Odin as a limitless power source with the ability to create bridges between distant locations by folding space between the locations.

Both devices in their respective universes have been associated with the Red Skull and the mad god Thanos in their quests for power.

Touching the Cosmic Cube allows the wielder, gloved or not the ability to petition the Cube (assuming a good connection to the entity within) to perform feats of reality-alteration similar to wish-fulfillment. However, since the entity within is young and inexperienced such alterations include subconscious thoughts which often undermine the powers and abilities given. Both the Red Skull and Thanos failed in their bids for power due to their subconscious fears.

Touching the Tesseract is a more dangerous proposition. Since the scope of its full powers are known only to Odin, it is probably safer to touch the device only when necessary and preferably with protective equipment.

Are gloves enough? We are never told why it reacts the way it does when Schmidt touches it. It is possible he was transported to a distant realm of the device's choosing or of the wielder's unconscious desire.

Schmidt wore gloves. Didn't help him...

It is clear the device allows the user to open doorways between locations, but whether these doorways can span both time and space is currently unknown. Even if it is limited to space transport, distance does not appear to be a limiting agent allowing armies to be moved from one location to another instantly.

Marvel Earth-616 (the canon comic universe)

The Cosmic Cube - is the name of a fictional object that appears in the Marvel Universe. The concept was created by Stan Lee and Jack Kirby and first appeared in Tales of Suspense #79 (July 1966)

The Cosmic Cube was thought to have been created by Advanced Idea Mechanics (AIM) and been integral to the development of several of their more formidable developments including MODOK and the Super-Adaptoid.

It is later revealed the Cosmic Cube is a containment vessel for an alien being of immense cosmic power gestating until its birth. In its gestating form it is capable of of utilizing its powers in the name of the person touching it. The Cosmic Cube on Earth will eventually evolve and name itself Kubik.

Another matured Cosmic Cube found on the Skrull homeworld is called The Shaper of Worlds. His powers are consistent with most beings with this level of power including the Molecule Man and the Beyonder who were also matured aspects of Cosmic Cubes.

The Skrull matured Shaper of Worlds, calming the future cosmic being Kubik, one of the Cosmic Cubes of Earth

The Shaper is an alien matter-energy construct with unknown, and potentially incalculable physical power.

He has the ability to restructure finite pockets of reality and to alter the molecular configuration of persons and objects. He is also capable of intergalactic and interdimensional teleportation, and empathic perception.

The Shaper's intelligence is immeasurable, but lacking a creative imagination, the Shaper must use the mind of another sentient being as a template for his transformations of worlds.

Marvel Earth-199999 (the Cinematic Marvel universe)

The Tesseract - The Tesseract is an enchanted object of unparalleled power that was once owned by Odin. Believed to be Asgardian in origin, the cube is based on the Cosmic Cube in the Marvel Comics continuity. It exists in the Marvel Cinematic Universe and features predominantly in Captain America: The First Avenger and The Avengers.

The device does not appear to have the reality-altering nature of the canon Cosmic Cube but its energy is both unique and apparently limitless.

It appears to be able to be replicated using technology and makes for very effective weapons.

There is also some hint that the energy used in the Tesseract is later replicated for use as part of the Stark antigravity and repulsor technologies.

The tesseract was discovered by Johann Schmidt (later known as the Red Skull) in a box behind Nidhogg in a sculptured mural of Yggdrasil, the World Tree. The device was located inside a church full of Viking warriors entombed within its walls.

Schmidt and scientist Arnim Zola harnessed the power of the Tesseract to be used as weapons against the Allies and the entire world.

Captain America foils Schmidt's plan to use the Tesseract to launch an aerial attack on the United States, and Schmidt disintegrates into light that shoots into space when he touches the Cube.

After Captain America crashes Schmidt's plane, the Cube is recovered by Howard Stark and falls into the hands of SHIELD for a time where they create new weapons utilizing its energy.

The device is ultimately taken by Thor back to the secret weapon stockpiles of Odin's trophy room likely awaiting its use in the final battle of Ragnarok.

The tesseract is also supposed to be a theory of transportation in a 4th dimension where the universe is bended for basically teleportation.
– CilanMay 24 '14 at 15:54

3

Note that your first screenshot appears to be of Schmidt holding the fake Tesseract right before he smashes it. I don't think he actually touched the real Tesseract until the end. It was in a box when he first saw it, then was handled with tongs after that in the lab.
– OmegacronMay 4 '15 at 19:21

In the comics, what the cube does is 'grant the wishes of' someone who touches it.

The only two people we ever see TOUCH it in the movies are Red Skull and Fury. When Red Skull does so, it teleports him away somewhere. It could be argued that what we wanted was to escape, or to be a god. Presumably we'll have to wait for a future movie to find out exactly what did happen.

But what does Nick Fury want? What has he been talking about in every movie he's shown up in? He wants there to be the Avengers.

At basics, the Cosmic Cube is container for a massive amount of primordial energy that grants whomever holds it the nigh-omnipotent ability to reshape reality. [Emphasis mine.]

This phrase "holds [the Cube]" could either be construed as "possesses [the Cube]" or "actually holds [the Cube] in his or her hands". The latter meaning clears this question up nicely.

From the same article, here's a panel from the comics featuring Red Skull holding the Cube through a glove:

And one of the commenters has asserted that "the Cube responds to the thoughts and wishes of the wielder".

My hunch is that it's possible to hold onto a Cosmic Cube with your bare hands without being harmed, and it will respond to the thoughts and wishes of whoever is holding it. The good guys in Marvel movies probably hold onto the Cube with prongs or special suitcases so that it will remain inert and not respond to their impulses.